Question

a 5.5 m long ladder is leaned against a wall.the ladder reaches the wall to a of 4.4 m.find the distance between the wall and the foot of the ladder

Answer 1

Answer:-

Given Information:-

Length of the Ladder = 5.5 m

Length of the wall = 4.4 m

To Find:-

$\large\tt{Distance \ between \ wall \\ and \ the \ foot \ of \ ladder.}$

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We Know,

Pythagoras Theorem:-

$\boxed{\large\tt{{(Hypotenuse)}^{2}={(Base)}^{2}+{(Altitude)}^{2}}}$

(See the attachment for making concept clear)

Here,

1. Hypotenuse = 5.5
2. Altitude = 4.4
3. Base is taken = x

Hence,

Let the distance between the foot of the ladder be $x$ metres.

ACCORDING TO THE QUESTION:-

$\tt{ {(5.5)}^{2} = {x}^{2} + {(4.4)}^{2} }$

(According to the formulae, we have set a linear equation to find the suitable result)

$\tt{\implies {(5.5)}^{2} = ({x}^{2}) + (4.4 \times 4.4)}$

(In the Right Hand Side, we have converted the exponential of of the numbers into multiplication form)

$\tt{\implies 30.25 = {x}^{2} + 19.36}$

(Product of the numbers. Changes can be seen in the Right Hand Side and the Left one too. 5.5² is now written)

$\tt{\implies {x}^{2} = 30.25-19.36}$

(Taken the numbers to the Right Hand Side and their will be the Operation)

$\tt{\implies x= \sqrt {10.89}}$

(We have now found the number after their Subtraction and also Given Radical Sign to the Right Hand Side and ^2 in x is demolished)

$\tt{\implies x = \sqrt {3.3 \times 3.3}}$

(Written that √10.89 = √3.3•3.3)

$\boxed{\tt\green{\implies x = 3.3}}$

(Answer)

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REQUIRED ANSWER:-

$\large\tt{{\therefore Distance \ between \ the \ wall \\ and \ the \ foot \ of \ the \ladder \ is \ 3.3 \ metres.}}$